For some reason I was worried that Liz Truss was going to be fierce. She's actually very pleasant, but always comes across as highly uncompromising in her politics, and it's probably a typical chauvinistic fallacy which makes me assume she'll try to tear me to shreds during her interview.

But she admits: "I am quite bolshy, sometimes. I like to get my own way, lets put it like that."

Getting her own way, in terms of becoming an MP at least, took Truss a while. First in 2001 in the West Yorkshire seat of Hemwsorth (solid Labour; no chance) and then in 2005 in nearby Calder Valley (marginal - close run thing with 1,000 votes in it.)

Finally she got the seat of South West Norfolk to fight in 2010 - securing her place in Parliament for as long as she wants it, but not without a fight from the local association who objected to what they saw as a Cameroon A-lister being parachuted in. How's she getting on with her constituents now?

"Things seem to be going pretty well, actually," she says. "And actually Norfolk is doing pretty well in the recession, because we have a lot of agricultural engineering. Eastern Europe is mechanising its agricultural sector and we're exporting machinery to them. It's one of those niche opportunities."

Even by MP standards Truss - who's 36 - seems ridiculously busy; obviously trying to win over the "turnip Taliban" in her constituency association who didn't want her to be their MP, but also rallying free-market Tories by founding the Thatcherite Free Enterprise Group (loved by right-wing think-tanks and the Tory press) and co-authoring a book about the future for the Conservative party, somewhat antagonistically titled "After The Coalition".

"There's a big market for ideas at the moment and if you look at what's going on in the Tory party, there's lots of different people making lots of cases," she says.

Her background is fascinating; comprehensively educated in Leeds and the daughter of a maths professor. The passion for maths has rubbed off - she talks a lot about the need for a major overhaul in how maths is taught for 16-18s. Her enthusiasm for maths veers on the obsessional, talking about a school in her patch that's just become an academy, where a bunch of Canadian maths teachers have been imported to up standards. "New ideas, new innovation, fantastic."

She's broadly supportive of Michael Gove's education reforms, particularly the English Baccalaureate which is in her words having a "huge impact on people's life chances". But she worries that 16-18 year-olds need better serving - "It's a gaping hole at the moment."

"I went to a school in south London last week to talk to students about why they weren't doing maths. The message isn't getting through about how valuable it is as something that helps you to get a job. I also think the problem with maths A-level is there's no intermediate option.

"In other countries you can do high-level maths or general maths, whereas we've just got all-or-nothing. We need to give people another option from 16-18. Not everyone is going to want to become a rocket scientist but that doesn't mean that maths isn't extremely useful.

"Schools receive 12% more per student for those doing media studies or psychology than they do for those doing maths. You could change that around, made a premium on doing maths."

Truss has become something of a critical friend of various ministers recently, persistently lobbying Michael Gove about the importance of maths. "I don't think that's been thought through."

She's prodding the government to do make maternity and paternity leave more flexible, and seems to have got her own way, if the Queen's Speech measures on parental leave have substance. How do her calls from the backbenches go down?

"Well," she says and pauses for a while. "I put my idea for the subject premium at education questions a few weeks ago and Michael Gove basically didn't say he was going to do it, which was disappointing. Of course ministers want to focus on what they're doing, but you need debate and you need ideas. And you need people making the case as well."

Even though she's fairly outspoken, Truss is seen as a contender for ministerial office. Having a comprehensive education must be a boost. What was her experience, going to school in Leeds?

"I think it was quite sporadic, there were some excellent teachers and some not very good teachers, and there was a lot of luck of the draw. At my school there was a sense of, 'Those interested in going to Oxford please see me after assembly,' rather than actually encouraging students. Laissez faire is how I'd put it, and there were a lot of talented students who could've been pushed harder.

"They did fine, but not as well as they could've done. And certainly having gone to Oxford, and seen some of the other students there, I wouldn't say the ones at my school were less capable. They could've been there. I was very disturbed to read in the Times Educational Supplement that only 50% of comprehensive teachers would recommend to their pupils that they consider Oxford. We should be bigging them up, rather than saying, 'It's not for the likes of you,' It is awful. Appalling."

Does she want to be elevated to junior ministerial level in a reshuffle, when it comes?

"Er..." There is a laugh and an even longer pause. "I'm enjoying what I'm doing at the moment, putting forward ideas, and the thing that interests me is getting things done. I would rather be a productive backbencher, than the alternative."

What's the alternative? "If I wasn't getting anywhere."

But don't you have to be a minister to get things done? "I don't think that is true. You saw in the budget that Ben Gummer's proposal about tax statements was taken forward. He's not a minister, he's just a backbencher with an idea. I think we live in quite a porous world now, where there's a huge public debate, there are lots of platforms to put forward ideas."